Boston public television giant WGBH­ received $4.2 million from the state’s film tax credit program last year alone for programs like “American Experience,” “Antiques Roadshow,” and “Nova.” And Watertown animation studio Soup2Nuts received about $300,000 in subsidies last year, mostly for the PBS series “WordGirl.”

“It has been very helpful for us to make our budget,” said WGBH spokeswoman Jeanne Hopkins. “That’s funding we would have to find elsewhere.”

The Massachusetts program offers companies $1 in film tax credits for every $4 they spend filming movies, television shows, and commercials in the state — including for PBS. Over the first five years, hundreds of productions qualified for more than $276 million in credits.

Romney campaign spokeswoman Andrea Saul said that unlike the federal government, Massachusetts had the money for the subsidies. She noted that Romney built a $2 billion rainy day fund in Massachusetts, while the federal government is running $1 trillion deficits.

But Michael Widmer, president of the Massachusetts Taxpayers Foundation and a critic of the film tax credits, said the state wasn’t exactly swimming in extra cash. He noted that Romney made $425 million in emergency budget cuts in November 2006, a year after enacting the film tax credit program.

The Corporation for Public Broadcasting receives about $450 million a year from the US government, which it then uses to support stations around the country.

“The point that Romney is making is that public television needs to be cut in order to help balance the budget is similar to the dynamic at the state level,” Widmer said. “Their own actions show that we didn’t have the resources to do this without cutting spending elsewhere.”

The Big Bird battle highlights the differences in how Republicans around the country have viewed federal funding for public broadcasting, compared with broader local subsidies for film and television production as a whole. In the debate, Romney said he would eliminate federal subsidies to PBS because the nation, burdened with trillions in debt, couldn’t afford it.

The Corporation for Public Broadcasting receives about $450 million a year from the US government, which it then uses to support stations around the country.

“I like PBS. I love Big Bird,” Romney said. “But . . . I’m not going to keep on spending money on things to borrow money from China to pay for it.”

For years, Republicans have tried to cut off funding for PBS, National Public Radio, and other public broadcasters because of the perception they have a liberal bias and compete with for-profit stations that don’t receive government aid.

By contrast, many Republicans — along with Democrats — have supported subsidies for the film and television industries at the state level in an effort to create jobs and boost tourism.

“It’s very bipartisan,” said Greg LeRoy, executive director of Good Jobs First, a nonprofit in Washington that is generally critical of economic development subsidies. “It’s the intersection between Hollywood and politics.”

Despite the “tax credit” name, the film program isn’t a conventional tax break. Many of the recipients already pay little or no income taxes in Massachusetts and don’t need tax credits to further reduce their bills. But like many states, Massachusetts allows companies to sell the credits back to the state or other taxpayers who do owe money, so even nonprofits like WGBH can convert the credits to cash.

It is not clear whether Romney had WGBH in mind when he approved the program.

One of the key architects of the law said Romney and his aides didn’t do much to craft the details, push lawmakers to pass it, or publicly tout the subsidy. “They certainly did not oppose it,” said Plymouth County Treasurer Thomas J. O’Brien, who was then a state representative. “But they weren’t that involved.”

Romney signed the bill into law just before Thanksgiving 2005, but did it without a public signing ceremony. In a press release at the time, Romney said the program would help boost movie and television production in the state. “Grab your popcorn and soda, because Massachusetts is ready for its close-up,” Romney said in the release.

But Romney’s statements about cutting off PBS funding at the presidential debate got more attention, and prompted “Sesame Street” fans and President Obama supporters to post pictures of Big Bird holding a sign “Will Work For Food” and jokingly call for a Million Muppet March.

WGBH, which carries “Sesame Street,” featured Big Bird on an LED screen on its building Friday visible from the Massachusetts Turnpike. The station received $7.4 million from the Corporation for Public Broadcasting in the last fiscal year, accounting for about 11 percent of its annual local operating budget. And WGBH was quick to note some smaller stations are even more reliant on federal funds to buy programs from WGBH and other providers.

“The federal funding is really important,” said Hopkins of WGBH. Without it, “the whole system would be in jeopardy.”